The present invention generally relates to wave guide filters and, more particularly, to odd elliptic function band-pass filters using multiple coupled high Q cavities.
The synthesis of multiple coupled high Q wave guide cavity filters has been outlined in the technical literature as represented by the following publications:
J. D. Rhodes, "The Generalized Direct-Coupled Cavity Linear Phase Filter," IEEE Transactions MTT, Volume MTT-18, No. 6, June 1970, pages 308-313; PA0 A. E. Atia et al., "Narrow-Bandpass Waveguide Filters," IEEE Transactions MTT, Volume MTT-20, No. 4, April 1972, pages 258-264; and PA0 A. E. Atia et al., "Narrow-Band Multiple-Coupled Cavity Synthesis," IEEE Transactions CAS, Volume CAS-21, No. 5, September 1974, pages 649-655.
The type of structures described in the foregoing publications can generate transfer functions t(s) of the form EQU t(s)=N(s)/D(s) (1)
where s=j(.omega.-1/.omega.), D(s) is a Hurwitz polynomial whose order equals that of the number of cavities, and N(s) is an even polynomial whose order 0 is EQU 0[N(s)].ltoreq.0[D(s)]-2
That is, an even order elliptic function band-pass filter response can be generated, but an odd order response cannot. For example, for a fifth-order transfer function, the maximum order of [N(s)]=2, whereas a true fifth-order elliptic function response must realize an even fourth-order [N(s)].
A third-order coupled wave guide cavity band-pass filter has been described by R. M. Kurzrok, "General Three-Resonator Filters in Waveguide," IEEE Transactions MTT, Volume MTT-14, 1966, pages 46 and 47. This type of filter may take either of the configurations shown in FIGS. 1a or 1b. While not shown in the drawing, the FIG. 1a configuration has all magnetic (positive) couplings with series couplings between successively numbered cavities 1 and 2 and between cavities 2 and 3 as well as a coupling between non-successively numbered cavities 1 and 3. The FIG. 1b configuration has the same order of couplings between successive and non-successive cavities, except one is negative. The voltage-loop current relationship is given by ##EQU1## where the numerator N(.lambda.) [.lambda.=.omega.-(1/.omega.)] of the voltage transfer function is expressed as EQU N(.lambda.).varies.(.lambda.M.sub.13 -M.sub.12 M.sub.23) (3)
The geometry of FIG. 1a (all positive couplings) then yields one real zero above the passband, while the geometry of FIG. 1b (one negative coupling) generates the zero below the passband. Both these responses are asymmetrical. While useful in certain applications, the conversion of these responses to the symmetrical odd order elliptic function filter response would be a positive achievement.